Subgroups — Dic₉×#10597243 #36344795

Order 21780.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#10597243	C₂	1	1	yes	maximal, characteristic
2	Dic₃×#10597243	—	3	1	no	maximal
3	C₉×#10597243	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁²×Dic₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×#10597243	D₃	1	1	yes	characteristic
6	C₄×#10597243	—	9	1	no	Hall
7	C₂×C₉×C₁₁²	C₂×C₅	1	1	yes	characteristic
8	Dic₉×C₁₁⋊C₅	—	11	12	no	maximal
9	C₃×#10597243	Dic₃	1	1	yes	characteristic
10	C₁₁²×Dic₃	—	3	1	no	—
11	C₂×#10597243	D₉	1	1	yes	characteristic
12	C₉×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₁₁⋊C₅	—	11	12	no	—
14	C₂×C₃×C₁₁²	C₅×D₃	1	1	yes	characteristic
15	Dic₃×C₁₁⋊C₅	—	33	12	no	—
16	#10597243	Dic₉	1	1	yes	characteristic, direct product factor, Hall
17	C₉×C₁₁⋊C₅	—	11	12	no	—
18	C₄×C₁₁²	—	9	1	no	Hall
19	C₁₁×Dic₉	C₁₁⋊C₅	1	12	yes	complemented
20	C₃×C₁₁²	C₅×Dic₃	1	1	yes	characteristic
21	C₂×C₃×C₁₁⋊C₅	—	11	12	no	—
22	C₂×C₁₁²	C₅×D₉	1	1	yes	characteristic
23	C₄×C₁₁⋊C₅	—	99	12	no	—
24	C₂×C₉×C₁₁	C₂×C₁₁⋊C₅	1	12	yes	—
25	C₅×Dic₉	—	121	1	no	Hall
26	C₃×C₁₁⋊C₅	—	11	12	no	—
27	C₁₁×Dic₃	—	3	12	no	—
28	C₁₁²	C₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₁⋊C₅	—	11	12	no	—
30	C₉×C₁₁	C₄×C₁₁⋊C₅	1	12	yes	complemented
31	C₂×C₅×C₉	—	121	1	no	—
32	C₂×C₃×C₁₁	D₃×C₁₁⋊C₅	1	12	yes	—
33	C₅×Dic₃	—	363	1	no	—
34	C₁₁⋊C₅	—	11	12	no	—
35	C₅×C₉	—	121	1	no	Hall
36	C₄×C₁₁	—	9	12	no	—
37	Dic₉	#10597243	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₁₁	Dic₃×C₁₁⋊C₅	1	12	yes	—
39	C₂×C₃×C₅	—	121	1	no	—
40	C₂×C₁₁	D₉×C₁₁⋊C₅	1	12	yes	—
41	C₄×C₅	—	1089	1	no	Hall
42	C₂×C₉	C₂×#10597243	1	1	yes	characteristic
43	C₃×C₅	—	121	1	no	—
44	Dic₃	—	3	1	no	—
45	C₁₁	Dic₉×C₁₁⋊C₅	1	12	yes	complemented
46	C₂×C₅	—	121	1	no	—
47	C₉	C₄×#10597243	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	D₃×#10597243	1	1	yes	characteristic
49	C₅	—	121	1	no	Sylow
50	C₄	—	9	1	no	Sylow
51	C₃	Dic₃×#10597243	1	1	yes	characteristic
52	C₂	D₉×#10597243	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉×#10597243
commutator, hypocenter	C₉×C₁₁²	C₄×C₅
Frattini	C₂×C₃	D₃×#10597243
Fitting, cosocle	C₂×C₉×C₁₁²	C₂×C₅
socle	C₂×C₃×C₁₁²	C₅×D₃
prime radical	C₂×C₃×#10597243	D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₉×#10597243	C₄	semidirect
4. C₁₁²×Dic₉	C₅	semidirect
12. C₉×C₁₁²	C₄×C₅	semidirect
16. #10597243	Dic₉	direct (N × H)
19. C₁₁×Dic₉	C₁₁⋊C₅	semidirect
28. C₁₁²	C₅×Dic₉	semidirect
30. C₉×C₁₁	C₄×C₁₁⋊C₅	semidirect
37. Dic₉	#10597243	direct (N × H)
45. C₁₁	Dic₉×C₁₁⋊C₅	semidirect
47. C₉	C₄×#10597243	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#10597243	2
Dic₃×#10597243	3
C₁₁²×Dic₉	5
Dic₉×C₁₁⋊C₅	11

Subgroups — Dic9×#10597243 #36344795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉×#10597243 #36344795